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Math Help - Polynomial Expansion Using Pascals Triangle

  1. #1
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    Polynomial Expansion Using Pascals Triangle

    Heres the question followed by the textbook answer from the back.



    Im stuck on how it got the answer. Ive just done about 5 others in the same way, but this one doesn't seem to give me the right answer.

    I got:

    1+12x+30x^2+40x^3+30x^4+12x^5+2x^6

    I did the correct method i think.
    Heres the row of the pascal triangle i used:

    1 6 15 20 15 6 1

    So i basicly did:

    (1)(1^6)(2x^0) + (6)(1^5)(2x^1) + (15)(1^4)(2x^2)... etc and simplified. I really don't understand how i got the answer wrong. Any suggestions?
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  2. #2
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    Hello,

    Quote Originally Posted by nugiboy View Post
    Heres the question followed by the textbook answer from the back.



    Im stuck on how it got the answer. Ive just done about 5 others in the same way, but this one doesn't seem to give me the right answer.

    I got:

    1+12x+30x^2+40x^3+30x^4+12x^5+2x^6

    I did the correct method i think.
    Heres the row of the pascal triangle i used:

    1 6 15 20 15 6 1

    So i basicly did:

    (1)(1^6)({\color{red}(}2x{\color{red})}^0) + (6)(1^5)({\color{red}(}2x{\color{red})}^1) + (15)(1^4)({\color{red}(}2x{\color{red})}^2)... etc and simplified. I really don't understand how i got the answer wrong. Any suggestions?
    The mistakes are in red
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  3. #3
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    Remember that it is \left(1+\left(2x\right)\right)^6!
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